Details

Time bar (total: 56.7s)

sample263.0ms

Algorithm
intervals
Results
96.0ms517×body80nan
29.0ms293×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02128
14928
215228
363228
4391928
done500028

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize42.0ms

Local error

Found 4 expressions with local error:

6.7b
(* n (pow (/ l Om) 2.0))
6.8b
(/ (* l l) Om)
9.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
24×add-sqr-sqrt
23×pow1
20×associate-*r/ associate-*r* add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate-*l* associate--l+ 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 → 112
Calls
4 calls:
49.0ms
(* n (pow (/ l Om) 2.0))
22.0ms
(/ (* l l) Om)
229.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
141.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.8s

Counts
4 → 12
Calls
4 calls:
207.0ms
(* n (pow (/ l Om) 2.0))
32.0ms
(/ (* l l) Om)
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify554.0ms

Counts
124 → 124
Iterations

Useful iterations: done (550.0ms)

IterNodesCost
03443129
110172953
done50002685

prune817.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.6b

localize49.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.7b
(* n (pow (/ l Om) 2.0))
9.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite497.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×pow1 add-sqr-sqrt associate-*r*
22×associate-*r/
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 pow-exp associate--l+ 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 → 119
Calls
4 calls:
64.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
38.0ms
(* n (pow (/ l Om) 2.0))
218.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
171.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.9s

Counts
4 → 12
Calls
4 calls:
560.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
190.0ms
(* n (pow (/ l Om) 2.0))
1.8s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify623.0ms

Counts
131 → 131
Iterations

Useful iterations: done (613.0ms)

IterNodesCost
03503452
110193256
done50002963

prune944.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.6b

localize36.0ms

Local error

Found 4 expressions with local error:

4.3b
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
6.3b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.1b
(* (* (* 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*))))
20.0b
(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*)))))

rewrite796.0ms

Algorithm
rewrite-expression-head
Rules
91×add-exp-log
63×prod-exp
26×associate-*r/
25×pow1
22×add-cbrt-cube
18×pow-exp
16×flip3-- flip--
13×pow-prod-down
12×frac-sub cbrt-unprod
10×sub-neg
9×pow-to-exp div-exp add-log-exp
8×distribute-rgt-in add-sqr-sqrt *-un-lft-identity distribute-lft-in associate-*r*
6×add-cube-cbrt sqrt-div associate--l+
4×sqrt-pow1 associate--r+
3×diff-log
2×associate-*l* *-commutative
1×associate--l- pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 123
Calls
4 calls:
91.0ms
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
246.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
273.0ms
(* (* (* 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*))))
180.0ms
(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*)))))

series11.2s

Counts
4 → 12
Calls
4 calls:
950.0ms
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
571.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s
(* (* (* 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*))))
7.8s
(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*)))))

simplify625.0ms

Counts
135 → 135
Iterations

Useful iterations: done (619.0ms)

IterNodesCost
03295843
110144632
done50004224

prune816.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.6b

localize36.0ms

Local error

Found 4 expressions with local error:

4.3b
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
5.8b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
9.1b
(* (* (* 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*)))))
20.0b
(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*))))))

rewrite589.0ms

Algorithm
rewrite-expression-head
Rules
38×associate-*r/
24×add-sqr-sqrt
23×pow1
21×add-exp-log
18×associate-*l*
16×flip3-- *-un-lft-identity flip--
15×unpow-prod-down add-cbrt-cube
14×distribute-rgt-in add-cube-cbrt distribute-lft-in
12×sub-neg pow-prod-down frac-sub
10×times-frac prod-exp
9×add-log-exp
8×associate-*r* associate--r+
7×cbrt-unprod
6×sqrt-div associate--l+
4×sqrt-pow1 unswap-sqr
3×diff-log
2×pow-exp *-commutative sqr-pow
1×associate--l- pow-to-exp pow1/2 div-exp sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 127
Calls
4 calls:
111.0ms
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
71.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
225.0ms
(* (* (* 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*)))))
172.0ms
(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*))))))

series8.9s

Counts
4 → 12
Calls
4 calls:
711.0ms
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
362.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.4s
(* (* (* 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*)))))
6.4s
(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*))))))

simplify399.0ms

Counts
139 → 139
Iterations

Useful iterations: done (393.0ms)

IterNodesCost
03595357
110355119
done50004619

prune616.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.2b

regimes598.0ms

Accuracy

9.2% (8.9b remaining)

Error of 29.4b against oracle of 20.6b and baseline of 30.3b

bsearch159.0ms

Steps
ItersRangePoint
9
2.1211728365061636e-97
1.710291495840365e-91
1.898225491734353e-94

simplify23.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03883
15083
done5083

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.7s15067×body80nan
1.5s9221×body80valid