Details

Time bar (total: 1.3m)

sample189.0ms

Algorithm
intervals
Results
53.0ms458×body80nan
32.0ms278×body80valid

simplify2.4s

Counts
1 → 1
Iterations
IterNodes
done5000
43869
3632
2152
149
021

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize39.0ms

Local error

Found 4 expressions with local error:

4.6b
(* n (pow (/ l Om) 2.0))
5.9b
(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
6.1b
(* (* n (pow (/ l Om) 2.0)) (- U* U))
19.2b
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×add-sqr-sqrt pow1 associate-*r*
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×unpow-prod-down add-cube-cbrt
13×pow-prod-down
10×times-frac cbrt-unprod
6×associate-*r/
5×associate-*l*
4×sqrt-pow1 associate-*l/ pow-exp add-log-exp unswap-sqr
3×*-commutative
2×distribute-rgt-in pow-to-exp sub-neg distribute-lft-in flip3-+ sqrt-div div-exp flip-+ sqr-pow
1×flip3-- pow1/2 sqrt-prod div-inv flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 103
Calls
4 calls:
22.0ms
(* n (pow (/ l Om) 2.0))
498.0ms
(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
61.0ms
(* (* n (pow (/ l Om) 2.0)) (- U* U))
480.0ms
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series17.7s

Counts
4 → 12
Calls
4 calls:
220.0ms
(* n (pow (/ l Om) 2.0))
1.9s
(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
617.0ms
(* (* n (pow (/ l Om) 2.0)) (- U* U))
15.0s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify2.3s

Counts
115 → 115
Iterations
IterNodes
done5002
24126
1718
0260

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.0b

localize44.0ms

Local error

Found 4 expressions with local error:

4.5b
(* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om)))))
4.6b
(* n (pow (/ l Om) 2.0))
5.9b
(* (* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om))))) U)
19.2b
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om))))) U))

rewrite11.7s

Algorithm
rewrite-expression-head
Rules
28×pow1
26×add-exp-log
24×associate-*r*
23×add-sqr-sqrt
20×add-cbrt-cube
17×*-un-lft-identity
15×unpow-prod-down pow-prod-down add-cube-cbrt
13×prod-exp
10×times-frac cbrt-unprod
6×associate-*r/
5×associate-*l*
4×sqrt-pow1 associate-*l/ add-log-exp unswap-sqr
3×flip3-+ *-commutative flip-+
2×sqrt-div pow-exp sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in pow1/2 div-exp sqrt-prod div-inv distribute-lft-out
Counts
4 → 98
Calls
4 calls:
3.1s
(* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om)))))
21.0ms
(* n (pow (/ l Om) 2.0))
4.2s
(* (* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om))))) U)
4.3s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om))))) U))

series8.5s

Counts
4 → 12
Calls
4 calls:
1.8s
(* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om)))))
214.0ms
(* n (pow (/ l Om) 2.0))
2.1s
(* (* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om))))) U)
4.3s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (cbrt (- U* U)) (* (cbrt (- U* U)) (* n (pow (/ l Om) 2.0)))) (cbrt (- U* U))) (* (* 2.0 l) (/ l Om))))) U))

simplify1.9s

Counts
110 → 110
Iterations
IterNodes
done5000
23054
1567
0212

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.5b

localize64.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (pow (/ l Om) 2.0) n)
6.1b
(* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n))
7.7b
(* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- (* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n)) (- (* l (* 2.0 (/ l Om))) t)))
19.2b
(sqrt (* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- (* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n)) (- (* l (* 2.0 (/ l Om))) t))) (cbrt U)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
48×pow1
44×prod-exp
40×associate-*l*
32×pow-prod-down
31×add-sqr-sqrt
25×add-cbrt-cube
23×unpow-prod-down *-un-lft-identity
19×add-cube-cbrt
17×cbrt-unprod
16×associate-*l/
13×pow-exp
12×associate-*r/
11×flip3-- flip--
10×cube-div cbrt-prod cbrt-div times-frac
9×pow-to-exp
8×cube-prod frac-sub
7×sqrt-pow1 associate-*r*
6×sqrt-div
4×div-exp add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in *-commutative sqr-pow
2×sub-neg distribute-lft-out-- associate--r- difference-of-squares
1×cube-mult pow1/2 unpow3 sqrt-prod div-inv
Counts
4 → 148
Calls
4 calls:
26.0ms
(* (pow (/ l Om) 2.0) n)
94.0ms
(* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n))
399.0ms
(* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- (* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n)) (- (* l (* 2.0 (/ l Om))) t)))
892.0ms
(sqrt (* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- (* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n)) (- (* l (* 2.0 (/ l Om))) t))) (cbrt U)))

series9.1s

Counts
4 → 12
Calls
4 calls:
340.0ms
(* (pow (/ l Om) 2.0) n)
562.0ms
(* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n))
2.6s
(* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- (* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n)) (- (* l (* 2.0 (/ l Om))) t)))
5.6s
(sqrt (* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- (* (pow (cbrt (- U* U)) 3) (* (pow (/ l Om) 2.0) n)) (- (* l (* 2.0 (/ l Om))) t))) (cbrt U)))

simplify479.0ms

Counts
160 → 160
Iterations
IterNodes
done5000
1989
0340

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.8b

localize46.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (pow (/ l Om) 2.0) n)
7.0b
(* (- (* (* (cbrt U) (cbrt U)) (* 2.0 n))) (- (* (/ l Om) (* 2.0 l)) t))
9.9b
(* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- U* U)) (* (pow (/ l Om) 2.0) n))
19.2b
(sqrt (* (+ (* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- U* U)) (* (pow (/ l Om) 2.0) n)) (* (- (* (* (cbrt U) (cbrt U)) (* 2.0 n))) (- (* (/ l Om) (* 2.0 l)) t))) (cbrt U)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
163×add-exp-log
124×prod-exp
56×add-cbrt-cube
46×cbrt-unprod
34×pow1
25×add-sqr-sqrt
24×associate-*l*
21×pow-prod-down
15×unpow-prod-down *-un-lft-identity add-cube-cbrt
14×pow-exp
12×associate-*l/ associate-*r/
10×times-frac
7×pow-to-exp div-exp associate-*r*
6×flip3-- sqrt-div flip--
5×unswap-sqr
4×frac-add add-log-exp
3×*-commutative
2×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 sqr-pow
1×distribute-lft-neg-out distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in flip3-+ pow1/2 sqrt-prod flip-+ div-inv
Counts
4 → 142
Calls
4 calls:
32.0ms
(* (pow (/ l Om) 2.0) n)
82.0ms
(* (- (* (* (cbrt U) (cbrt U)) (* 2.0 n))) (- (* (/ l Om) (* 2.0 l)) t))
470.0ms
(* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- U* U)) (* (pow (/ l Om) 2.0) n))
600.0ms
(sqrt (* (+ (* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- U* U)) (* (pow (/ l Om) 2.0) n)) (* (- (* (* (cbrt U) (cbrt U)) (* 2.0 n))) (- (* (/ l Om) (* 2.0 l)) t))) (cbrt U)))

series7.7s

Counts
4 → 12
Calls
4 calls:
376.0ms
(* (pow (/ l Om) 2.0) n)
1.0s
(* (- (* (* (cbrt U) (cbrt U)) (* 2.0 n))) (- (* (/ l Om) (* 2.0 l)) t))
618.0ms
(* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- U* U)) (* (pow (/ l Om) 2.0) n))
5.7s
(sqrt (* (+ (* (* (* (* (cbrt U) (cbrt U)) (* 2.0 n)) (- U* U)) (* (pow (/ l Om) 2.0) n)) (* (- (* (* (cbrt U) (cbrt U)) (* 2.0 n))) (- (* (/ l Om) (* 2.0 l)) t))) (cbrt U)))

simplify617.0ms

Counts
154 → 154
Iterations
IterNodes
done5000
11070
0351

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 20.1b

regimes2.0s

Accuracy

8.1% (11.3b remaining)

Error of 31.2b against oracle of 19.9b and baseline of 32.2b

bsearch560.0ms

Steps
ItersRangePoint
8
1643461432666.1616
564507482701451.8
31641216734603.953
7
2.640163512511391e-200
7.070440059353413e-199
1.0087251072023538e-199
7
-4.012884601640852e-79
-2.582920869966925e-81
-9.014626965436398e-81

simplify24.0ms

Iterations
IterNodes
done123
3123
2122
1107
074

end0.0ms

sample6.8s

Algorithm
intervals
Results
3.3s14656×body80nan
1.5s9110×body80valid