Details

Time bar (total: 9.8s)

sample76.0ms

Algorithm
intervals
Results
24.0ms294×body80nan
15.0ms120×body160valid
8.0ms136×body80valid

simplify126.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110
done500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(pow (/ t l) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 114
Calls
4 calls:
6.0ms
(pow (/ Om Omc) 2.0)
6.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
44.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (/ Om Omc) 2.0)
65.0ms
(pow (/ t l) 2.0)
19.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
344.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify57.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
07091289
120871218
250011206
done50011206

prune514.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(pow (/ t l) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 114
Calls
4 calls:
6.0ms
(pow (/ Om Omc) 2.0)
6.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
46.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series502.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (/ Om Omc) 2.0)
68.0ms
(pow (/ t l) 2.0)
19.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
348.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify55.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
07091289
120871218
250011206
done50011206

prune594.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.5b

localize23.0ms

Local error

Found 4 expressions with local error:

9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
30.0b
(cbrt (pow (/ t l) 2.0))
30.0b
(cbrt (pow (/ t l) 2.0))
30.0b
(cbrt (pow (/ t l) 2.0))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
55×times-frac
51×cbrt-prod
46×*-un-lft-identity
45×unpow-prod-down
40×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 125
Calls
4 calls:
43.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
5.0ms
(cbrt (pow (/ t l) 2.0))
5.0ms
(cbrt (pow (/ t l) 2.0))
5.0ms
(cbrt (pow (/ t l) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
350.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
287.0ms
(cbrt (pow (/ t l) 2.0))
285.0ms
(cbrt (pow (/ t l) 2.0))
283.0ms
(cbrt (pow (/ t l) 2.0))

simplify50.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
05232252
112332182
250012146
done50012146

prune827.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.5b

localize39.0ms

Local error

Found 4 expressions with local error:

9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))))))))
24.5b
(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
30.0b
(cbrt (pow (/ t l) 2.0))
30.0b
(cbrt (pow (/ t l) 2.0))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
47×times-frac
43×cbrt-prod
40×*-un-lft-identity
37×unpow-prod-down
34×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 117
Calls
4 calls:
43.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))))))))
5.0ms
(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
5.0ms
(cbrt (pow (/ t l) 2.0))
5.0ms
(cbrt (pow (/ t l) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
348.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))))))))
285.0ms
(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
284.0ms
(cbrt (pow (/ t l) 2.0))
282.0ms
(cbrt (pow (/ t l) 2.0))

simplify60.0ms

Counts
129 → 129
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
06463209
115173104
250013044
done50013044

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.5b

regimes813.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.4b and baseline of 10.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02012
12012
done2012

end0.0ms

sample1.8s

Algorithm
intervals
Results
475.0ms7897×body80nan
442.0ms3765×body160valid
253.0ms4235×body80valid