Details

Time bar (total: 20.2s)

sample75.0ms

Algorithm
intervals
Results
21.0ms270×body80nan
19.0ms126×body160valid
10.0ms130×body80valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5001
51583
4292
3108
251
129
016

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
28×sqrt-prod difference-of-squares
27×unpow-prod-down
9×add-exp-log
8×associate-/l* sqr-pow
7×distribute-lft-out--
6×pow1 add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square div-exp pow-exp associate-/l/
1×pow-to-exp cbrt-undiv asin-acos clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 134
Calls
4 calls:
69.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
8.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
56.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series645.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
68.0ms
(pow (/ Om Omc) 2.0)
13.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
300.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.8s

Counts
146 → 146
Iterations
IterNodes
done5001
21767
1605
0276

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
8.2b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite72.0ms

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
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×sqrt-div div-exp pow-exp 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 → 155
Calls
4 calls:
56.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
7.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series672.0ms

Counts
4 → 12
Calls
4 calls:
428.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
88.0ms
(pow (/ Om Omc) 2.0)
19.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
137.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.5s

Counts
167 → 167
Iterations
IterNodes
done5000
21746
1619
0312

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.8b

localize61.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
7.8b
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
8.2b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
8.2b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
2.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
2.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series639.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
181.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
139.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
154.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.3s

Counts
84 → 84
Iterations
IterNodes
done5000
42341
3643
2263
1129
075

prune555.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.8b

localize45.0ms

Local error

Found 4 expressions with local error:

8.1b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
14.1b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
14.1b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
14.1b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
101×add-sqr-sqrt
76×sqrt-prod
56×*-un-lft-identity
47×cbrt-prod
44×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
7×div-inv
6×distribute-lft-out-- sqr-pow
5×pow1 rem-sqrt-square
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 132
Calls
4 calls:
56.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series945.0ms

Counts
4 → 12
Calls
4 calls:
395.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
188.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
204.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
158.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.6s

Counts
144 → 144
Iterations
IterNodes
done5000
21554
1568
0330

prune1.3s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 8.8b

regimes968.0ms

Accuracy

0% (0.1b remaining)

Error of 9.8b against oracle of 9.7b and baseline of 9.8b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done15
015

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s3791×body160valid
1.0s7907×body80nan
532.0ms4209×body80valid