Details

Time bar (total: 36.3s)

sample416.0ms

Algorithm
intervals
Results
52.0ms481×body80nan
22.0ms298×body80valid

simplify127.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114
done500114

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize21.0ms

Local error

Found 4 expressions with local error:

6.9b
(* n (pow (/ l Om) 2.0))
8.0b
(/ (* l l) Om)
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite276.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
23×pow1
20×add-cube-cbrt *-un-lft-identity associate-*r/ associate-*r* add-cbrt-cube
15×unpow-prod-down
13×times-frac
12×prod-diff pow-prod-down
11×prod-exp
10×distribute-rgt-in flip3-- distribute-lft-in associate--l+ flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×expm1-log1p-u sub-neg sqrt-pow1 associate-*l* log1p-expm1-u add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv pow-exp *-commutative div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l*
Counts
4 → 132
Calls
4 calls:
25.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(/ (* l l) Om)
128.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
106.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts
4 → 12
Calls
4 calls:
150.0ms
(* n (pow (/ l Om) 2.0))
19.0ms
(/ (* l l) Om)
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify50.0ms

Counts
144 → 144
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010791948
150011746
done50011746

prune582.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.4b

localize18.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.9b
(* n (pow (/ l Om) 2.0))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×add-exp-log
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×add-cbrt-cube
19×prod-exp
15×unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac associate--l+ cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×pow-to-exp div-exp sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 157
Calls
4 calls:
46.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
23.0ms
(* n (pow (/ l Om) 2.0))
129.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
96.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.8s

Counts
4 → 12
Calls
4 calls:
375.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
147.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify46.0ms

Counts
169 → 169
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012292461
150012136
done50012136

prune565.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.9b

localize23.0ms

Local error

Found 4 expressions with local error:

13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log expm1-log1p-u sqrt-pow1 frac-sub add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 93
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
180.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

series5.2s

Counts
4 → 12
Calls
4 calls:
63.0ms
(cbrt (/ l Om))
63.0ms
(cbrt (/ l Om))
60.0ms
(cbrt (/ l Om))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

simplify72.0ms

Counts
105 → 105
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06091159
125641115
250011109
done50011109

prune579.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.9b

localize29.0ms

Local error

Found 4 expressions with local error:

13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

rewrite360.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-prod
24×pow1
20×associate-*r/
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
12×sqrt-div pow-prod-down
10×flip3-- flip--
8×sqrt-pow1 frac-sub
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×cbrt-div pow1/2 pow1/3 sqrt-prod div-inv
Counts
4 → 90
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
176.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))
177.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

series10.1s

Counts
4 → 12
Calls
4 calls:
68.0ms
(cbrt (/ l Om))
67.0ms
(cbrt (/ l Om))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

simplify75.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06091730
125521662
250011658
done50011658

prune772.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.9b

regimes488.0ms

Accuracy

16.1% (8.0b remaining)

Error of 30.2b against oracle of 22.2b and baseline of 31.8b

bsearch144.0ms

Steps
ItersRangePoint
10
5.9142685482905006e+106
1.1318126295060305e+120
4.212962541612979e+117

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04762
14762
done4762

end0.0ms

sample2.7s

Algorithm
intervals
Results
967.0ms14744×body80nan
606.0ms9169×body80valid