Details

Time bar (total: 26.6s)

sample107.0ms

Algorithm
intervals
Results
33.0ms135×body80valid
25.0ms275×body80nan
20.0ms121×body160valid

simplify3.6s

Counts
1 → 1
Iterations
IterNodes
done5000
62611
5774
4250
3102
251
129
016

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize55.0ms

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

rewrite155.0ms

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:
6.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
80.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
62.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(pow (/ Om Omc) 2.0)
14.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
237.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
386.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify3.0s

Counts
146 → 146
Iterations
IterNodes
done5000
34080
21306
1595
0276

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.9b

localize48.0ms

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 (pow (/ t l) 2.0) 2.0 1.0)))
0.5b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
12.1b
(sqrt (fma (pow (/ t l) 2.0) 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:
5.0ms
(pow (/ Om Omc) 2.0)
74.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
2.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series618.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(pow (/ Om Omc) 2.0)
378.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
19.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
137.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.6s

Counts
167 → 167
Iterations
IterNodes
done5001
32939
21172
1609
0312

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.9b

localize48.0ms

Local error

Found 4 expressions with local error:

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

series600.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
166.0ms
(sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
121.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
135.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.5s

Counts
84 → 84
Iterations
IterNodes
done5000
53983
41188
3488
2228
1129
075

prune769.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.9b

localize69.0ms

Local error

Found 4 expressions with local error:

12.1b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
12.1b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
12.1b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
13.3b
(cbrt (* (sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cube-unmult rem-cbrt-cube
1×cbrt-prod pow1/3
Counts
4 → 58
Calls
4 calls:
1.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
8.0ms
(cbrt (* (sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))

series689.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
149.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
169.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
206.0ms
(cbrt (* (sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))

simplify2.2s

Counts
70 → 70
Iterations
IterNodes
done5020
53455
41077
3454
2211
1120
070

prune689.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 12.9b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done15
015

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.4s3756×body160valid
1.3s8012×body80nan
561.0ms4244×body80valid