Details

Time bar (total: 2.6m)

sample275.0ms

Algorithm
intervals
Results
74.0ms449×body80nan
29.0ms309×body80valid

simplify2.4s

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.1b

localize43.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (* n (pow (/ l Om) 2.0)) (- U* U))
5.8b
(* n (pow (/ l Om) 2.0))
7.1b
(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
17.6b
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite1.2s

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:
57.0ms
(* (* n (pow (/ l Om) 2.0)) (- U* U))
21.0ms
(* n (pow (/ l Om) 2.0))
571.0ms
(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
530.0ms
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series17.4s

Counts
4 → 12
Calls
4 calls:
486.0ms
(* (* n (pow (/ l Om) 2.0)) (- U* U))
188.0ms
(* n (pow (/ l Om) 2.0))
2.0s
(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
14.8s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify2.0s

Counts
115 → 115
Iterations
IterNodes
done5002
24127
1716
0260

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.2b

localize53.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
6.0b
(* n (pow (/ l Om) (/ 2.0 2)))
7.1b
(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
17.6b
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite3.4s

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
25×add-sqr-sqrt pow1 associate-*r*
24×add-cbrt-cube
20×pow-exp
17×*-un-lft-identity
15×unpow-prod-down add-cube-cbrt
13×pow-prod-down cbrt-unprod
10×pow-to-exp times-frac div-exp
6×associate-*r/
5×associate-*l*
4×sqrt-pow1 associate-*l/ add-log-exp unswap-sqr
3×*-commutative
2×distribute-rgt-in sub-neg distribute-lft-in flip3-+ sqrt-div flip-+ sqr-pow
1×flip3-- pow1/2 sqrt-prod div-inv flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 120
Calls
4 calls:
165.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
30.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.7s
(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
1.6s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series15.6s

Counts
4 → 12
Calls
4 calls:
387.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
183.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.3s
(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
13.8s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify1.6s

Counts
132 → 132
Iterations
IterNodes
done5000
24565
1833
0295

prune915.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 21.7b

localize78.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2)))
5.8b
(* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
7.1b
(* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
17.6b
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite11.4s

Algorithm
rewrite-expression-head
Rules
1007×add-exp-log
775×prod-exp
322×pow-exp
171×div-exp
111×pow-to-exp
40×rec-exp 1-exp
34×associate-*r*
32×add-cbrt-cube
25×pow1
22×add-sqr-sqrt unpow-prod-down *-un-lft-identity
20×add-cube-cbrt
19×cbrt-unprod
18×times-frac
13×pow-prod-down
9×cbrt-prod
6×associate-*r/
4×sqrt-pow1 associate-*l/ add-log-exp
3×associate-*l* *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in flip3-+ sqrt-div flip-+
1×flip3-- pow1/2 sqrt-prod div-inv flip-- distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 305
Calls
4 calls:
49.0ms
(* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2)))
487.0ms
(* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
5.3s
(* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
5.6s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series16.0s

Counts
4 → 12
Calls
4 calls:
329.0ms
(* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2)))
785.0ms
(* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
1.8s
(* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
13.1s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify424.0ms

Counts
317 → 317
Iterations
IterNodes
done5000
11668
0551

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 20.7b

localize114.0ms

Local error

Found 4 expressions with local error:

7.4b
(* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))
17.6b
(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))
17.6b
(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))
17.6b
(sqrt (* (sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))) (sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))))

rewrite8.8s

Algorithm
rewrite-expression-head
Rules
466×pow1
307×pow-prod-down
264×sqrt-pow1
176×associate-*r/
144×sqrt-div
108×associate-*l/
85×flip3-- flip--
68×frac-sub
37×pow-prod-up
36×frac-times
27×pow-sqr
19×pow1/2
16×add-cbrt-cube add-exp-log
8×prod-exp cbrt-unprod
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
3×sqrt-prod
1×pow2 rem-sqrt-square pow-plus associate-*r* associate-*l* *-commutative
Counts
4 → 220
Calls
4 calls:
990.0ms
(* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))
882.0ms
(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))
881.0ms
(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))
6.0s
(sqrt (* (sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))) (sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))))

series1.1m

Counts
4 → 12
Calls
4 calls:
1.6s
(* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))
21.9s
(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))
21.6s
(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))
21.6s
(sqrt (* (sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))) (sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))))

simplify1.0s

Counts
232 → 232
Iterations
IterNodes
done5003
23879
1922
0392

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 20.4b

regimes1.0s

Accuracy

40.6% (5.5b remaining)

Error of 27.0b against oracle of 21.5b and baseline of 30.8b

bsearch288.0ms

Steps
ItersRangePoint
9
2.4256268370447587e-303
5.292323950905223e-294
2.469810196486197e-303
7
-5.769464553509918e-44
-4.636171290286106e-46
-7.411448247083684e-46

simplify9.0ms

Iterations
IterNodes
done75
275
174
054

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.1s14813×body80nan
937.0ms9174×body80valid