Details

Time bar (total: 23.1s)

sample125.0ms

Algorithm
intervals
Results
29.0ms117×body160valid
28.0ms225×body80nan
17.0ms139×body80valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
done5001
51551
4277
3101
249
129
016

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
8.9b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×unpow-prod-down add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×add-cbrt-cube pow-exp 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 → 106
Calls
4 calls:
9.0ms
(pow (/ t l) 2.0)
9.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
73.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))

series698.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(pow (/ t l) 2.0)
117.0ms
(pow (/ Om Omc) 2.0)
33.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
457.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))

simplify1.3s

Counts
118 → 118
Iterations
IterNodes
done5000
22370
1858
0352

prune902.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.4b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.5b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
95×sqrt-prod
82×times-frac
65×*-un-lft-identity
51×add-cube-cbrt
28×difference-of-squares
27×unpow-prod-down
11×associate-/l*
9×add-exp-log
8×sqr-pow
7×distribute-lft-out--
6×pow1 associate-/r* add-cbrt-cube sqrt-div
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×pow-to-exp cbrt-undiv rem-sqrt-square asin-acos sqrt-undiv clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 151
Calls
4 calls:
10.0ms
(pow (/ Om Omc) 2.0)
86.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
4.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series886.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(pow (/ Om Omc) 2.0)
527.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
25.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
258.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.2s

Counts
163 → 163
Iterations
IterNodes
done5000
22235
1699
0325

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.5b

localize103.0ms

Local error

Found 4 expressions with local error:

15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.5b
(sqrt (pow (/ Om Omc) 2.0))
17.5b
(sqrt (pow (/ Om Omc) 2.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-prod
30×add-sqr-sqrt unpow-prod-down
22×*-un-lft-identity add-cube-cbrt
20×times-frac
8×rem-sqrt-square
6×cbrt-prod
4×pow1 cbrt-div add-cbrt-cube add-exp-log add-log-exp sqr-pow
2×sqrt-pow1 flip3-+ pow1/2 pow1/3 flip-+ div-inv
Counts
4 → 86
Calls
4 calls:
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.0ms
(sqrt (pow (/ Om Omc) 2.0))
8.0ms
(sqrt (pow (/ Om Omc) 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
342.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
370.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
445.0ms
(sqrt (pow (/ Om Omc) 2.0))
428.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify2.0s

Counts
98 → 98
Iterations
IterNodes
done5000
33828
2952
1378
0177

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.0b
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.6b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.6b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
92×cbrt-prod
82×times-frac
59×*-un-lft-identity
41×add-cube-cbrt
36×difference-of-squares
33×sqrt-prod
18×unpow-prod-down
9×distribute-lft-out-- sqr-pow
6×associate-/r/
5×pow1
4×add-cbrt-cube add-exp-log add-log-exp
3×rem-sqrt-square cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×sqrt-pow1
1×asin-acos pow1/2 sqrt-div
Counts
4 → 133
Calls
4 calls:
1.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
49.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
29.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
25.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
44.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
544.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
454.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
484.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.5s

Counts
145 → 145
Iterations
IterNodes
done5002
34069
21245
1538
0296

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.5b

regimes1.7s

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.5b and baseline of 10.6b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done19
119
017

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s4146×body80valid
809.0ms3854×body160valid
807.0ms8096×body80nan