Details

Time bar (total: 24.3s)

sample138.0ms

Algorithm
intervals
Results
54.0ms252×body80nan
36.0ms141×body160valid
16.0ms115×body80valid

simplify3.7s

Counts
1 → 1
Iterations
IterNodes
done5022
64794
51100
4363
3142
261
132
016

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
8.3b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
84×*-un-lft-identity
81×times-frac
77×add-sqr-sqrt
53×add-cube-cbrt
26×sqrt-prod
18×add-cbrt-cube add-exp-log difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
11×distribute-lft-out
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×associate-/r* prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×rem-sqrt-square flip3-+ flip-+ associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 163
Calls
4 calls:
14.0ms
(* (/ t l) (/ t l))
47.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
75.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (/ t l) (/ t l))
129.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
19.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
191.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify2.2s

Counts
175 → 175
Iterations
IterNodes
done5000
22202
1722
0268

prune954.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize45.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt (/ t l)) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l)))))))
13.2b
(cbrt (/ t l))
13.2b
(cbrt (/ t l))
13.2b
(cbrt (/ t l))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
48×times-frac
42×add-sqr-sqrt
39×cbrt-prod
35×add-cube-cbrt
26×sqrt-prod
8×difference-of-squares
5×pow1 distribute-lft-out
4×add-cbrt-cube add-exp-log insert-posit16 div-inv add-log-exp
3×cbrt-div pow1/3
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 108
Calls
4 calls:
56.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt (/ t l)) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l)))))))
1.0ms
(cbrt (/ t l))
1.0ms
(cbrt (/ t l))
1.0ms
(cbrt (/ t l))

series440.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt (/ t l)) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l)))))))
90.0ms
(cbrt (/ t l))
90.0ms
(cbrt (/ t l))
81.0ms
(cbrt (/ t l))

simplify3.1s

Counts
120 → 120
Iterations
IterNodes
done5000
31817
2701
1330
0189

prune645.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l))))))))
8.3b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l)))))))
13.2b
(cbrt (/ t l))
13.2b
(cbrt (/ t l))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
39×times-frac
35×add-sqr-sqrt
28×add-cube-cbrt
26×cbrt-prod sqrt-prod
8×difference-of-squares
5×pow1 distribute-lft-out
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×div-inv
2×rem-sqrt-square cbrt-div pow1/3 associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 94
Calls
4 calls:
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l))))))))
45.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l)))))))
1.0ms
(cbrt (/ t l))
1.0ms
(cbrt (/ t l))

series439.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l))))))))
282.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l)))))))
62.0ms
(cbrt (/ t l))
65.0ms
(cbrt (/ t l))

simplify2.7s

Counts
106 → 106
Iterations
IterNodes
done5000
32973
2900
1406
0224

prune877.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.3b

localize87.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (/ (cbrt t) l))) (/ t l))))))))
4.7b
(cbrt (/ (cbrt t) l))
8.3b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (/ (cbrt t) l))) (/ t l)))))))
13.2b
(cbrt (/ t l))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity times-frac
44×cbrt-prod
41×add-sqr-sqrt
34×add-cube-cbrt
26×sqrt-prod
8×difference-of-squares
5×pow1 distribute-lft-out
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×div-inv
2×rem-sqrt-square cbrt-div pow1/3 associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 103
Calls
4 calls:
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (/ (cbrt t) l))) (/ t l))))))))
2.0ms
(cbrt (/ (cbrt t) l))
50.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (/ (cbrt t) l))) (/ t l)))))))
1.0ms
(cbrt (/ t l))

series628.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (/ (cbrt t) l))) (/ t l))))))))
182.0ms
(cbrt (/ (cbrt t) l))
341.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (* (cbrt t) (cbrt (/ 1 l))) (cbrt (/ t l))) (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (/ (cbrt t) l))) (/ t l)))))))
81.0ms
(cbrt (/ t l))

simplify2.9s

Counts
115 → 115
Iterations
IterNodes
done5009
34050
21140
1525
0297

prune938.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 9.3b

regimes433.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done18
118
015

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s3813×body160valid
1.1s8238×body80nan
433.0ms4187×body80valid