Details

Time bar (total: 22.2s)

sample117.0ms

Algorithm
intervals
Results
46.0ms275×body80nan
24.0ms121×body160valid
13.0ms135×body80valid

simplify1.9s

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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))))
0.5b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
11.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite156.0ms

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:
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))))
75.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
60.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series864.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(pow (/ Om Omc) 2.0)
24.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
313.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
427.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.6s

Counts
146 → 146
Iterations
IterNodes
done5001
21765
1605
0276

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.9b

localize33.0ms

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 (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.5b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
12.1b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite93.0ms

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:
11.0ms
(pow (/ Om Omc) 2.0)
70.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series690.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(pow (/ Om Omc) 2.0)
418.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
14.0ms
(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
21739
1619
0312

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.9b

localize75.0ms

Local error

Found 4 expressions with local error:

5.5b
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
5.5b
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
12.1b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
12.1b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite8.0ms

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))

series671.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
204.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
146.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
132.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.6s

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

prune733.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.9b

localize63.0ms

Local error

Found 4 expressions with local error:

11.8b
(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))))
17.2b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
17.2b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
17.2b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite75.0ms

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:
65.0ms
(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))

series1.1s

Counts
4 → 12
Calls
4 calls:
453.0ms
(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))))
221.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
218.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
195.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.9s

Counts
144 → 144
Iterations
IterNodes
done5000
21554
1568
0330

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.9b

regimes971.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done15
015

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.6s8012×body80nan
975.0ms3756×body160valid
568.0ms4244×body80valid