Details

Time bar (total: 38.2s)

sample101.0ms

Algorithm
intervals
Results
39.0ms556×body80nan
24.0ms295×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
02128
14928
215127
360127
4304827
done500027

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.8b

localize20.0ms

Local error

Found 4 expressions with local error:

7.1b
(/ (* l l) Om)
8.1b
(* n (pow (/ l Om) 2.0))
10.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite117.0ms

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:
3.0ms
(/ (* l l) Om)
14.0ms
(* n (pow (/ l Om) 2.0))
52.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
42.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (* l l) Om)
142.0ms
(* 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*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.5s

Counts
144 → 144
Iterations

Useful iterations: 2 (741.0ms)

IterNodesCost
03893995
110743803
244993329
done50003329

prune644.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.3b

localize20.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.1b
(* n (pow (/ l Om) 2.0))
10.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite139.0ms

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:
26.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.0ms
(* n (pow (/ l Om) 2.0))
52.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
41.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
373.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
138.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify831.0ms

Counts
169 → 169
Iterations

Useful iterations: done (825.0ms)

IterNodesCost
04435038
112234647
done50004148

prune639.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.2b

localize22.0ms

Local error

Found 4 expressions with local error:

4.4b
(* n (pow (/ l Om) (/ 2.0 2)))
6.5b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.8b
(* (* (* 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*))))
18.5b
(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*)))))

rewrite228.0ms

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:
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
84.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
66.0ms
(* (* (* 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*))))
54.0ms
(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*)))))

series6.8s

Counts
4 → 12
Calls
4 calls:
159.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
362.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s
(* (* (* 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*))))
5.0s
(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*)))))

simplify494.0ms

Counts
186 → 186
Iterations

Useful iterations: done (484.0ms)

IterNodesCost
04797307
113505730
done50015512

prune702.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.3b

localize26.0ms

Local error

Found 4 expressions with local error:

4.4b
(* n (pow (/ l Om) (/ 2.0 2)))
7.5b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.8b
(* (* (* 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*)))))
18.5b
(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*))))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
41×*-un-lft-identity
39×add-cube-cbrt
30×unpow-prod-down associate-*r/ prod-diff
29×add-exp-log
25×associate-*r*
23×pow1
21×distribute-rgt-in distribute-lft-in associate-*l*
20×times-frac
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×flip3-- flip--
10×associate--l+
8×frac-sub cbrt-unprod unswap-sqr
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u add-log-exp sqr-pow
3×*-commutative
2×pow-to-exp div-exp div-inv
1×pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 174
Calls
4 calls:
17.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
24.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
64.0ms
(* (* (* 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*)))))
48.0ms
(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*))))))

series6.5s

Counts
4 → 12
Calls
4 calls:
161.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
327.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.3s
(* (* (* 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*)))))
4.7s
(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*))))))

simplify653.0ms

Counts
186 → 186
Iterations

Useful iterations: done (645.0ms)

IterNodesCost
04916325
112755900
done50015316

prune743.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.3b

regimes541.0ms

Accuracy

10.2% (9.3b remaining)

Error of 30.0b against oracle of 20.7b and baseline of 31.0b

bsearch486.0ms

Steps
ItersRangePoint
10
5.761168895017816e+38
6.252508614851994e+54
5.849773459839704e+38
8
5.196301700147731e-22
1.1700142316632325e-17
1.1504183261425661e-17
8
1.43410142141466e-189
6.5416925795497415e-186
5.754288137534979e-186
8
-5.835929371065793e-123
-6.527847966246e-127
-5.852286491090293e-126

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
053193
173154
done73154

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.1s15073×body80nan
640.0ms9245×body80valid