Details

Time bar (total: 4.6m)

sample236.0ms

Algorithm
intervals
Results
110.0ms481×body80nan
80.0ms303×body80valid

simplify2.3s

Counts
1 → 1
Iterations
IterNodes
done5000
43618
3693
2157
150
021

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.3b

localize72.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* n (pow (/ l Om) 2)) (- U U*))
6.5b
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
6.7b
(/ (* l l) Om)
19.2b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite10.0s

Algorithm
rewrite-expression-head
Rules
4043×add-sqr-sqrt
1524×prod-diff
1256×*-un-lft-identity
1170×unswap-sqr
1126×associate-*l*
1092×times-frac
985×associate-*r*
782×add-cube-cbrt
768×distribute-rgt-in distribute-lft-in
697×difference-of-squares
429×unpow-prod-down
382×associate--l+
243×distribute-lft-out--
184×*-commutative
166×swap-sqr
77×unpow2 sqr-pow
49×sqrt-prod
32×add-exp-log div-inv
28×pow1
23×add-cbrt-cube
22×associate-*r/
16×prod-exp
15×pow-prod-down associate-/l*
11×flip3-- flip--
10×cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* div-exp
2×cbrt-undiv pow-exp
1×pow-to-exp clear-num frac-2neg pow1/2
Counts
4 → 1824
Calls
4 calls:
171.0ms
(* (* n (pow (/ l Om) 2)) (- U U*))
3.4s
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
28.0ms
(/ (* l l) Om)
6.1s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.7s

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (* n (pow (/ l Om) 2)) (- U U*))
598.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
24.0ms
(/ (* l l) Om)
2.0s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify6.5s

Counts
1836 → 1836
Iterations
IterNodes
done5001
02812

prune16.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.1b

localize78.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* (cbrt n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))
5.6b
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
6.7b
(/ (* l l) Om)
17.0b
(sqrt (* (* (cbrt n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

rewrite17.8s

Algorithm
rewrite-expression-head
Rules
8537×add-sqr-sqrt
2884×associate-*r/
2774×*-un-lft-identity
2507×times-frac
2436×prod-diff
2347×associate-*l*
2319×unswap-sqr
2225×frac-times
2062×associate-*r*
1981×add-cube-cbrt
1237×difference-of-squares
1224×distribute-rgt-in distribute-lft-in
1220×frac-sub
1122×flip3-- flip--
930×associate-/l*
903×associate-/r*
671×swap-sqr
640×associate-*l/
612×sqrt-div
395×distribute-lft-out--
382×associate--l+
335×*-commutative
316×clear-num
301×frac-2neg
107×div-inv
47×sqrt-prod
41×add-cbrt-cube
39×add-exp-log
30×un-div-inv
24×pow1
21×cbrt-unprod
19×prod-exp
12×pow-prod-down
11×cbrt-prod
6×cbrt-undiv sub-neg div-exp
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1
1×pow1/2
Counts
4 → 4288
Calls
4 calls:
6.2s
(* (* (cbrt n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))
629.0ms
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
21.0ms
(/ (* l l) Om)
10.1s
(sqrt (* (* (cbrt n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

series22.3s

Counts
4 → 12
Calls
4 calls:
1.6s
(* (* (cbrt n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))
185.0ms
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
36.0ms
(/ (* l l) Om)
20.5s
(sqrt (* (* (cbrt n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

simplify10.8s

Counts
4300 → 4300
Iterations
IterNodes
done7229
07229

prune45.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.8b

localize104.0ms

Local error

Found 4 expressions with local error:

5.1b
(* n (* (/ l Om) (/ l Om)))
5.6b
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
6.7b
(/ (* l l) Om)
12.3b
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

rewrite11.9s

Algorithm
rewrite-expression-head
Rules
1718×associate-*r/
1416×frac-times
726×add-sqr-sqrt
625×associate-/l*
612×flip3-- sqrt-div flip--
610×frac-sub
603×associate-/r*
557×*-un-lft-identity
521×add-cube-cbrt
393×associate-*l/
211×clear-num
201×frac-2neg
165×associate-*r*
149×times-frac
146×associate-*l*
98×unswap-sqr
52×add-cbrt-cube add-exp-log
51×sqrt-prod
46×swap-sqr
28×cbrt-prod
25×prod-exp cbrt-unprod
21×pow1
20×un-div-inv
18×prod-diff
16×distribute-lft-out--
15×*-commutative
12×difference-of-squares
11×distribute-rgt-in distribute-lft-in
10×cbrt-undiv div-exp pow-prod-down
9×div-inv
5×rem-sqrt-square
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×sub-neg sqrt-pow1
1×pow1/2
Counts
4 → 1378
Calls
4 calls:
137.0ms
(* n (* (/ l Om) (/ l Om)))
645.0ms
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
39.0ms
(/ (* l l) Om)
10.6s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

series12.2s

Counts
4 → 12
Calls
4 calls:
99.0ms
(* n (* (/ l Om) (/ l Om)))
155.0ms
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
34.0ms
(/ (* l l) Om)
11.9s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

simplify9.0s

Counts
1390 → 1390
Iterations
IterNodes
done5000
04202

prune18.5s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 11.0b

localize138.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (- t (* 2 (/ l (/ Om l)))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))
5.1b
(* n (* (/ l Om) (/ l Om)))
5.6b
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
12.3b
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

rewrite14.3s

Algorithm
rewrite-expression-head
Rules
3887×add-sqr-sqrt
2382×associate-*r/
2306×frac-times
1764×*-un-lft-identity
1334×add-cube-cbrt
1220×frac-sub
1122×flip3-- flip--
1095×times-frac
1078×prod-diff
1074×associate-/l*
1051×associate-*l*
969×associate-/r* associate-*r*
873×unswap-sqr
649×associate-*l/
612×sqrt-div
463×difference-of-squares
339×clear-num
323×frac-2neg
213×distribute-lft-out--
206×swap-sqr
194×associate--l+
116×associate-/r/
65×*-commutative
60×div-inv
51×sqrt-prod
47×add-cbrt-cube add-exp-log
32×un-div-inv
28×cbrt-prod
24×prod-exp cbrt-unprod
22×distribute-rgt-in distribute-lft-in associate--r+
21×pow1
10×fma-neg pow-prod-down
9×add-log-exp
8×cbrt-undiv div-exp
6×sub-neg
5×rem-sqrt-square
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×diff-log
2×sqrt-pow1
1×associate--l- pow1/2
Counts
4 → 3021
Calls
4 calls:
2.4s
(- (- t (* 2 (/ l (/ Om l)))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))
145.0ms
(* n (* (/ l Om) (/ l Om)))
662.0ms
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
10.5s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

series12.5s

Counts
4 → 12
Calls
4 calls:
389.0ms
(- (- t (* 2 (/ l (/ Om l)))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))
96.0ms
(* n (* (/ l Om) (/ l Om)))
165.0ms
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
11.8s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))

simplify11.4s

Counts
3033 → 3033
Iterations
IterNodes
done5432
05432

prune38.9s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 11.0b

regimes2.2s

Accuracy

0% (5.6b remaining)

Error of 18.7b against oracle of 13.1b and baseline of 18.7b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done42
142
033

end0.0ms

sample8.8s

Algorithm
intervals
Results
4.9s15269×body80nan
2.5s9207×body80valid