Details

Time bar (total: 2.4m)

sample346.0ms

Algorithm
intervals
Results
123.0ms483×body80nan
70.0ms286×body80valid

simplify944.0ms

Counts
1 → 1
Iterations
IterNodes
43429
3795
2222
192
021

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.1b

localize44.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ n (/ Om l))
5.6b
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
5.9b
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
20.6b
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))

rewrite491.0ms

Algorithm
rewrite-expression-head
Rules
1916×times-frac
843×add-sqr-sqrt
814×*-un-lft-identity
812×add-cube-cbrt
580×associate-*l*
102×div-inv
47×add-cbrt-cube add-exp-log
26×associate-*r/
25×pow1
18×cbrt-undiv div-exp
15×associate-/r/
14×distribute-rgt-in distribute-lft-in
13×associate-/r* pow-prod-down prod-exp cbrt-unprod
7×unswap-sqr
6×associate-*r*
4×sqrt-pow1 flip3-- sqrt-div frac-add insert-posit16 flip-- add-log-exp
3×associate-/l*
2×frac-times sub-neg flip3-+ *-commutative flip-+
1×clear-num frac-2neg pow1/2 associate-*l/ sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 745
Calls
4 calls:
6.0ms
(/ n (/ Om l))
236.0ms
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
39.0ms
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
180.0ms
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))

series3.6s

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ n (/ Om l))
518.0ms
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
173.0ms
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
2.9s
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))

simplify2.6s

Counts
757 → 757
Iterations
IterNodes
17052
01378

prune12.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.3b

localize66.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ Om (* l l))
5.6b
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
7.9b
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
20.6b
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*)))))))))

rewrite432.0ms

Algorithm
rewrite-expression-head
Rules
3160×times-frac
1371×add-sqr-sqrt
1318×*-un-lft-identity
1312×add-cube-cbrt
931×associate-*l*
354×cbrt-prod
125×div-inv
71×add-exp-log
45×add-cbrt-cube
32×div-exp
26×associate-*r/
25×pow1
20×prod-exp
17×cbrt-undiv
14×distribute-rgt-in distribute-lft-in associate-/r/ cbrt-unprod
13×pow-prod-down unswap-sqr
6×associate-*r*
4×sqrt-pow1 flip3-- sqrt-div frac-add insert-posit16 flip-- add-log-exp
3×rec-exp 1-exp associate-/l*
2×frac-times sub-neg flip3-+ *-commutative flip-+
1×clear-num associate-/r* frac-2neg pow1/2 associate-*l/ sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 1059
Calls
4 calls:
6.0ms
(/ Om (* l l))
172.0ms
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
47.0ms
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
152.0ms
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*)))))))))

series2.6s

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ Om (* l l))
436.0ms
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
356.0ms
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
1.7s
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*)))))))))

simplify2.7s

Counts
1071 → 1071
Iterations
IterNodes
17683
01533

prune18.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.6b

localize291.0ms

Local error

Found 4 expressions with local error:

3.1b
(* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))
5.6b
(* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
7.9b
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
20.6b
(sqrt (* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*)))))))))

rewrite456.0ms

Algorithm
rewrite-expression-head
Rules
3157×times-frac
1373×add-sqr-sqrt
1320×*-un-lft-identity
1312×add-cube-cbrt
934×associate-*l*
354×cbrt-prod
124×div-inv
68×add-exp-log
42×add-cbrt-cube
30×div-exp associate-*r/
27×pow1
20×prod-exp
15×distribute-rgt-in cbrt-undiv distribute-lft-in
14×pow-prod-down associate-/r/ cbrt-unprod unswap-sqr
10×associate-*r*
6×frac-add
5×flip3-- flip--
4×sqrt-pow1 sqrt-div insert-posit16 add-log-exp
3×rec-exp flip3-+ 1-exp *-commutative flip-+
2×frac-times sub-neg
1×pow1/2 associate-*l/ sqrt-prod distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 1063
Calls
4 calls:
62.0ms
(* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))
162.0ms
(* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
43.0ms
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
144.0ms
(sqrt (* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*)))))))))

series2.8s

Counts
4 → 12
Calls
4 calls:
373.0ms
(* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))
449.0ms
(* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
333.0ms
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
1.7s
(sqrt (* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*)))))))))

simplify2.5s

Counts
1075 → 1075
Iterations
IterNodes
17659
01525

prune18.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 20.3b

localize95.0ms

Local error

Found 4 expressions with local error:

3.1b
(* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*)))))))
5.6b
(* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*)))))))))
9.5b
(* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*))
20.6b
(sqrt (* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*))))))))))

rewrite604.0ms

Algorithm
rewrite-expression-head
Rules
8813×times-frac
3785×add-sqr-sqrt
3660×*-un-lft-identity
3647×add-cube-cbrt
3345×cbrt-prod
2494×associate-*l*
283×div-inv
68×add-exp-log
38×add-cbrt-cube
30×div-exp associate-*r/
29×unswap-sqr
27×pow1
20×prod-exp
15×distribute-rgt-in cbrt-undiv distribute-lft-in
14×pow-prod-down associate-/r/ cbrt-unprod
10×associate-*r*
6×frac-add
5×flip3-- flip--
4×sqrt-pow1 sqrt-div insert-posit16 add-log-exp
3×rec-exp flip3-+ 1-exp *-commutative flip-+
2×frac-times sub-neg
1×pow1/2 associate-*l/ sqrt-prod distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 2638
Calls
4 calls:
61.0ms
(* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*)))))))
165.0ms
(* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*)))))))))
73.0ms
(* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*))
141.0ms
(sqrt (* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*))))))))))

series3.1s

Counts
4 → 12
Calls
4 calls:
398.0ms
(* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*)))))))
471.0ms
(* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*)))))))))
563.0ms
(* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*))
1.7s
(sqrt (* U (* 2 (* n (+ (/ -2 (* (/ 1 l) (/ Om l))) (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ (* (cbrt n) (cbrt n)) (/ 1 (* (cbrt (cbrt l)) (cbrt (cbrt l))))) 1) (* (/ (/ (cbrt n) (/ Om (cbrt (cbrt l)))) (/ 1 l)) (- U U*))))))))))

simplify5.5s

Counts
2650 → 2650
Iterations
IterNodes
111017
02189

prune1.0m

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 20.1b

regimes1.5s

Accuracy

28.8% (5.5b remaining)

Error of 26.8b against oracle of 21.3b and baseline of 29.0b

bsearch4.0ms

simplify26.0ms

Iterations
IterNodes
289
189
067

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.6s14894×body80nan
1.5s9147×body80valid