Details

Time bar (total: 21.8s)

sample187.0ms

Algorithm
intervals
Results
67.0ms118×body160valid
57.0ms299×body80nan
29.0ms138×body80valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done2008
62008
51100
4363
3142
261
132
016

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (/ t l) (/ t l)) (/ t l))
0.6b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
8.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
81×times-frac
78×*-un-lft-identity
74×add-sqr-sqrt
59×add-cube-cbrt
36×associate-*l*
21×sqrt-prod
15×distribute-rgt-out
14×difference-of-squares
13×associate-*r* distribute-lft-out
11×add-cbrt-cube add-exp-log
7×pow1 div-inv
5×associate-/l*
4×flip3-+ associate-/r/ flip-+ insert-posit16 add-log-exp
3×frac-times associate-/r* associate-*l/
2×cbrt-undiv rem-sqrt-square distribute-lft1-in div-exp frac-add distribute-rgt1-in prod-exp cbrt-unprod unswap-sqr associate-/l/
1×asin-acos clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 count-2 sqrt-div div-sub pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 156
Calls
4 calls:
52.0ms
(* (+ (/ t l) (/ t l)) (/ t l))
27.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
16.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

series388.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (+ (/ t l) (/ t l)) (/ t l))
135.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
23.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
164.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

simplify1.6s

Counts
168 → 168
Iterations
IterNodes
done2001
32001
21954
1698
0302

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (sqrt (* (+ (/ t l) (/ t l)) (/ t l))) (sqrt (* (+ (/ t l) (/ t l)) (/ t l))))))))
8.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (sqrt (* (+ (/ t l) (/ t l)) (/ t l))) (sqrt (* (+ (/ t l) (/ t l)) (/ t l)))))))
17.6b
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
17.6b
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
23×sqrt-prod
19×add-sqr-sqrt
16×*-un-lft-identity times-frac
15×sqrt-div
13×add-cube-cbrt
11×pow1
6×frac-times associate-*l/ difference-of-squares
5×sqrt-pow1 flip3-+ flip-+
4×add-cbrt-cube frac-add add-exp-log insert-posit16 add-log-exp
3×pow1/2
2×rem-sqrt-square pow-prod-down associate-*r/ associate-/r/
1×asin-acos div-inv
Counts
4 → 81
Calls
4 calls:
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (sqrt (* (+ (/ t l) (/ t l)) (/ t l))) (sqrt (* (+ (/ t l) (/ t l)) (/ t l))))))))
15.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (sqrt (* (+ (/ t l) (/ t l)) (/ t l))) (sqrt (* (+ (/ t l) (/ t l)) (/ t l)))))))
20.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
21.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))

series679.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (sqrt (* (+ (/ t l) (/ t l)) (/ t l))) (sqrt (* (+ (/ t l) (/ t l)) (/ t l))))))))
467.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (sqrt (* (+ (/ t l) (/ t l)) (/ t l))) (sqrt (* (+ (/ t l) (/ t l)) (/ t l)))))))
91.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
88.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))

simplify1.4s

Counts
93 → 93
Iterations
IterNodes
done2006
32006
2699
1334
0188

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.7b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l))))))
0.7b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l)))))
8.9b
(sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
85×add-sqr-sqrt
72×*-un-lft-identity
65×add-cube-cbrt sqrt-prod
18×add-cbrt-cube sqrt-div add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1 frac-add
8×flip3-+ associate-/r/ flip-+ associate-/l*
6×associate-/r*
5×frac-times cbrt-undiv div-exp associate-*l/ associate-*r/ div-inv
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×associate-/l/
1×pow2 rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 185
Calls
4 calls:
12.0ms
(* (/ t l) (/ t l))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l))))))
30.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l)))))
25.0ms
(sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l))))

series262.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (/ t l) (/ t l))
10.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l))))))
139.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l)))))
85.0ms
(sqrt (+ (+ 1 (* (/ t l) (/ t l))) (* (/ t l) (/ t l))))

simplify900.0ms

Counts
197 → 197
Iterations
IterNodes
done2001
22001
1787
0325

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize55.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
17.6b
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
17.6b
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
17.6b
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
16×pow1
12×frac-times associate-*l/
8×sqrt-pow1 flip3-+ frac-add flip-+
4×add-sqr-sqrt *-un-lft-identity add-cbrt-cube pow1/2 pow-prod-down associate-*r/ add-exp-log add-cube-cbrt sqrt-prod insert-posit16 add-log-exp
Counts
4 → 76
Calls
4 calls:
10.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
19.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
18.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
19.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
78.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
76.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))
83.0ms
(sqrt (* (+ (/ t l) (/ t l)) (/ t l)))

simplify1.3s

Counts
88 → 88
Iterations
IterNodes
done2018
52018
41986
3477
2199
199
057

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

regimes517.0ms

Accuracy

98.2% (0.1b remaining)

Error of 5.9b against oracle of 5.8b and baseline of 10.5b

bsearch3.0ms

simplify7.0ms

Iterations
IterNodes
done30
130
025

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.5s8087×body80nan
1.5s3791×body160valid
790.0ms4209×body80valid