Details

Time bar (total: 1.1m)

sample266.0ms

Algorithm
intervals
Results
88.0ms291×body80valid
70.0ms464×body80nan

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
02128
14928
215427
364227
4323927
done500027

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize26.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.4b
(/ (* l l) Om)
21.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite437.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
30×prod-diff
26×add-sqr-sqrt *-un-lft-identity
25×pow1
24×add-cube-cbrt
23×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×associate--l+ cbrt-unprod
8×associate-*r* frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×times-frac div-exp associate-/r*
2×cbrt-undiv associate-*l* pow-exp *-commutative
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 141
Calls
4 calls:
61.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
192.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0ms
(/ (* l l) Om)
155.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.3s

Counts
4 → 12
Calls
4 calls:
558.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
37.0ms
(/ (* l l) Om)
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.4s

Counts
153 → 153
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
04114799
111424430
246863850
done50003850

prune848.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 23.4b

localize26.0ms

Local error

Found 4 expressions with local error:

6.4b
(* n (pow (/ l Om) 2.0))
6.5b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite474.0ms

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:
54.0ms
(* n (pow (/ l Om) 2.0))
70.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
202.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
140.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.5s

Counts
4 → 12
Calls
4 calls:
172.0ms
(* n (pow (/ l Om) 2.0))
508.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.1s

Counts
169 → 169
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
04435038
111974647
247024089
done50004089

prune961.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.0b

localize39.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) (/ 2.0 2)))
6.5b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
7.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
21.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite725.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
41×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
24×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×pow-exp
15×unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp associate--l+
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 174
Calls
4 calls:
29.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
199.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
296.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
187.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.2s

Counts
4 → 12
Calls
4 calls:
258.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
595.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify898.0ms

Counts
186 → 186
Iterations

Useful iterations: done (890.0ms)

IterNodesCost
04797307
112905730
done50005038

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.6b

localize68.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
6.5b
(* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
7.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
21.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
763×add-exp-log
575×prod-exp
210×pow-exp
129×div-exp
81×pow-to-exp
54×prod-diff
39×add-sqr-sqrt *-un-lft-identity
37×add-cube-cbrt
32×distribute-rgt-in distribute-lft-in
27×add-cbrt-cube
26×associate-*r/
25×pow1
22×associate--r+
16×flip3-- flip-- cbrt-unprod
15×associate--l+
13×pow-prod-down
12×frac-sub
10×sub-neg
9×add-log-exp
8×associate-*r*
6×sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u
3×fma-neg diff-log
2×associate-*l* *-commutative
1×associate--l- pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 301
Calls
4 calls:
148.0ms
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
1.1s
(* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
455.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
309.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series9.1s

Counts
4 → 12
Calls
4 calls:
688.0ms
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
384.0ms
(* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
6.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify655.0ms

Counts
313 → 313
Iterations

Useful iterations: done (640.0ms)

IterNodesCost
061419108
1150817555
done500115506

prune965.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.6b

regimes570.0ms

Accuracy

15% (8.0b remaining)

Error of 29.8b against oracle of 21.8b and baseline of 31.2b

bsearch175.0ms

Steps
ItersRangePoint
9
6.813752349909848e+88
1.387866107452373e+94
8.120471958061494e+92

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04592
15792
done5792

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.1s15327×body80nan
1.2s9227×body80valid