Details

Time bar (total: 24.2s)

sample143.0ms

Algorithm
intervals
Results
48.0ms245×body80nan
41.0ms127×body160valid
22.0ms129×body80valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
63283
5883
4308
3120
257
130
016

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.6b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
9.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
21×sqrt-prod
19×pow1
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 175
Calls
4 calls:
14.0ms
(* (/ t l) (/ t l))
21.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
20.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series220.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (/ t l) (/ t l))
44.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
131.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify979.0ms

Counts
187 → 187
Iterations
IterNodes
23051
1955
0330

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.6b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
9.6b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 157
Calls
4 calls:
22.0ms
(* (/ t l) (/ t l))
22.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
7.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series169.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (/ t l) (/ t l))
36.0ms
(* (/ Om Omc) (/ Om Omc))
16.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
85.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify711.0ms

Counts
169 → 169
Iterations
IterNodes
22692
1838
0264

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.0b

localize42.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
8.5b
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
9.6b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.6b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 sqrt-div add-exp-log add-log-exp
2×flip3-+ flip-+
Counts
4 → 56
Calls
4 calls:
1.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
1.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series257.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
34.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
103.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
80.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify4.7s

Counts
68 → 68
Iterations
IterNodes
46849
31326
2369
1153
073

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize83.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
8.5b
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ t l) (* 2 (/ t l))) 1)))))
9.6b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ t l) (* 2 (/ t l))) 1)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-prod
25×add-sqr-sqrt
19×*-un-lft-identity
16×times-frac add-cube-cbrt
8×pow1
6×difference-of-squares
5×rem-sqrt-square
4×sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log add-log-exp
3×sqrt-div
2×flip3-+ associate-/r/ flip-+
1×div-inv
Counts
4 → 74
Calls
4 calls:
1.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
3.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ t l) (* 2 (/ t l))) 1)))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
46.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ t l) (* 2 (/ t l))) 1)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
41.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ t l) (* 2 (/ t l))) 1)))))
75.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
151.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ t l) (* 2 (/ t l))) 1)))

simplify1.0s

Counts
86 → 86
Iterations
IterNodes
32636
2786
1347
0184

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

regimes656.0ms

Accuracy

98% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.1b

bsearch3.0ms

simplify9.0ms

Iterations
IterNodes
228
128
025

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.3s3801×body160valid
1.8s8076×body80nan
894.0ms4199×body80valid