Details

Time bar (total: 57.1s)

sample280.0ms

Algorithm
intervals
Results
114.0ms512×body80nan
37.0ms289×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02128
14928
215228
362728
4297828
done500028

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize41.0ms

Local error

Found 4 expressions with local error:

6.5b
(* n (pow (/ l Om) 2.0))
7.2b
(/ (* l l) Om)
10.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite351.0ms

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:
40.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(/ (* l l) Om)
148.0ms
(* (* (* 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*)))))

series9.5s

Counts
4 → 12
Calls
4 calls:
231.0ms
(* n (pow (/ l Om) 2.0))
23.0ms
(/ (* l l) Om)
1.8s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.4s

Counts
124 → 124
Iterations

Useful iterations: 2 (938.0ms)

IterNodesCost
03443129
19462953
238472649
done50002649

prune760.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.1b

localize38.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.5b
(* n (pow (/ l Om) 2.0))
10.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite455.0ms

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))
219.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
128.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.1s

Counts
4 → 12
Calls
4 calls:
605.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
198.0ms
(* n (pow (/ l Om) 2.0))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.2s

Counts
131 → 131
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
03493452
19733239
240912945
done50012945

prune831.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.4b

localize45.0ms

Local error

Found 4 expressions with local error:

3.7b
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
5.8b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
19.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite789.0ms

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:
68.0ms
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
216.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
288.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
211.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.1s

Counts
4 → 12
Calls
4 calls:
791.0ms
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
478.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.6s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify2.1s

Counts
135 → 135
Iterations

Useful iterations: 2 (939.0ms)

IterNodesCost
03285843
19504632
242674200
done50004200

prune530.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.4b

localize36.0ms

Local error

Found 4 expressions with local error:

11.6b
(cbrt (/ l Om))
11.6b
(cbrt (/ l Om))
11.6b
(cbrt (/ l Om))
19.3b
(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*)))))

rewrite186.0ms

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 sqrt-pow1 frac-sub add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 85
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
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*)))))

series5.4s

Counts
4 → 12
Calls
4 calls:
67.0ms
(cbrt (/ l Om))
61.0ms
(cbrt (/ l Om))
68.0ms
(cbrt (/ l Om))
5.2s
(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*)))))

simplify820.0ms

Counts
97 → 97
Iterations

Useful iterations: done (816.0ms)

IterNodesCost
02282019
15901867
223721798
done50001775

prune545.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.9b

regimes586.0ms

Accuracy

14.8% (8.8b remaining)

Error of 29.3b against oracle of 20.5b and baseline of 30.9b

bsearch143.0ms

Steps
ItersRangePoint
8
2.4864886162434826e+38
5.64601237047726e+41
1.1096816485837593e+40

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03371
14471
done4471

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.1s15106×body80nan
1.3s9162×body80valid